Fleischmann K, Greven A (1994)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 1994
Publisher: Springer Verlag (Germany)
Book Volume: 98
Pages Range: 517-566
Journal Issue: 4
URI: https://link.springer.com/article/10.1007/BF01192837
DOI: 10.1007/BF01192837
We study a countable system of interacting diffusions on the interval [0,1], indexed by a hierarchical group. A particular choice of the interaction guaranties, we are in the diffusive clustering regime. This means clusters of components with values either close to 0 or close to 1 grow on various different scales. However, single components oscillate infinitely often between values close to 0 and close to 1 in such a way that they spend fraction one of their time together and close to the boundary. The processes in the whole class considered and starting with a shift-ergodic initial law have the same qualitative properties (universality). © 1994 Springer-Verlag.
APA:
Fleischmann, K., & Greven, A. (1994). Diffusive clustering in an infinite system of hierarchically interacting diffusions. Probability Theory and Related Fields, 98(4), 517-566. https://dx.doi.org/10.1007/BF01192837
MLA:
Fleischmann, Klaus, and Andreas Greven. "Diffusive clustering in an infinite system of hierarchically interacting diffusions." Probability Theory and Related Fields 98.4 (1994): 517-566.
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